Cannot tell you what caused the humming noise.

Did you check if you aux fan is operational? One way to check is to have the car idled and turn on the A/C. The aux fan should come on after a short while. In addition, I believe you should be able to turn the fan by hand. If the fan does not move, than it is frozen.

Did you change the coolant? Since you mentioned you just purchased the car. You may want to check if air is trapped in the radiator hose as well.

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95 R129
04 Infiniti G35.5 BS
10 X204